Similar to car prices, we see the same mental rounding effect in rents. People will rent a home for $2100 or $2200, sometimes even $2150 for those truly dedicated to price finding, but hardly anyone rents an apartment for $2137.
You might get some of that if rent is raised by percentage. When I started my current job my salary was an integer multiple of $10,000. I got a raise at the end of my first year that was an integer percentage (3%, IIRC) so my salary was then an integer multiple of $100. The following year I got a raise again (it might have been an integer percentage, I don't recall) and my salary was just some random-looking integer.
Rent-controlled Berkeley apartments are allowed to increase rent by some fixed percentage, so maybe you can see this in your data? But I don't think the math would work out so cleanly.
The car pricing seems to be that some amount of people round 79,999 down to 70,000 when determining mileage and so cars with 79,999km on the odometer are penalised much less than cars with 80,000km.
I think the rent one is much more driven by "some landlords like round numbers for posting ads/doing their finances".
Source: my data for the city of Berkeley https://observablehq.com/@jwb/berkeley-rent-board-data#cell-...